The paper presents data on the synthesis, IR, electronic, X-ray photoelectron, and ESR spectroscopies of fullerene C60 molecular complexes with various types of donor compounds, namely, substituted tetrathiafulvalenes, aromatic hydrocarbons, diazodithiafulvalene, tetra-phenyldipyranylidene, tetrasulfur tetranitride, saturated amines, some metallocenes, and Co(II) and Mn(II) tetraphenylporphyrins. Crystal structures of some of these complexes are discussed. The degree of charge transfer in the complexes is evaluated from the shift of the F1u(4) C60 mode in the IR spectra. The factors responsible for the appearance of the symmetry-forbidden C60 vibrations and the splitting of the absorption bands of C60 in the complexes are considered. The electronic absorption spectra of some complexes show the decrease of the intensity of electron transitions of C60 at 420–530 nm and the appearance of new absorption bands attributed to charge transfer from the donor to C60. The dependences of the energy of charge transfer in the C60 complexes on ionisation and redox potentials of substituted tetra-thiafulvalenes are derived. Peculiarities of donor–acceptor interaction of donor molecules with the spherical C60 are considered.